A Note on the Use of the Woodbury Formula To Solve Cyclic Block Tri-Diagonal and Cyclic Blo
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Module 5 Unit 3 一、词性转换1.clone vt. 克隆n. 克隆出来的动物或植物2.tissue n.(生物的)组织;纸巾issue n.问题,争论;发行物3.exact adj.精确的,准确的→exactly adv.4.intention n.意图,目的→intend vt.5..anxiety n. 忧虑,焦虑,不安→anxious adj.6.adopt v. 采用;收养,领养adapt vt.. 适应;改编7.legal adj.法律许可的,合法的→illegal (反义词)→( il)legally adv.8.physician n.医师;内科医生→physic n.医药9.consequence n. 结果,后果→consequent adj.10.harvest vt.& n.收割/收获,收成11.sale n. 出售→sell vt..→salesman男销售员→saleswoman女销售员12.transform vt..使改变外观或性质(尤指向好的方向);使改变形态→transformation n.13..crime n.罪,罪行→criminal n.& adj.罪犯/犯罪的14.profession n. 职业→professional adj.15.original adj.& n.起初的;首创的,非复制的;独创的,新颖的/原著;有独创性的人→origin n.起源;出身→originally原来;独创性地16.judgement n.判断力;评价;(法律)判决→judge vt.& n.审判;判断/法官;裁判17.relation n.关系;亲戚→related adj.→relate vt.→relative adj.有关系的/n.亲戚→relatively adv.18.conduct vt.实施,指挥乐队→conductor n.19.majority n. 多数,大多数→major adj.主要的→minority n.(对应词)20.summary n. 总结;概要→summarize vt..21.consideration n. 仔细考虑;必须考虑的因素;体谅,顾及→consider vt→considerable adj.(数量、程度等)可观的,相当的22.hunger n.饥饿;饥荒→hungry adj.23.tasty adj.美味的,可口的→taste n.& vt.24.reliable adj.可信赖的,可依靠的→reliance n.→rely vt.25.accurate adj.准确的,精确的→accuracy n.→accurately adv.→inaccurate(反义词)26.brief adj.短时间的,短暂的;简洁的→briefly adv.27.actual adj.真实的,实际的→actually adv.28.agriculture n.农业→agricultural adj.29.favour vt..赞同;帮助;偏爱→favorable adj.赞同的;讨人喜欢的;有利的;→favorite n./adj.最喜爱的(东西)3o.genetics n.遗传学→genetically adv. 从基因上,与基因相关→gene基因n. 31.frighten vt..使惊吓,使惊恐→frightened/frightening adj.32.modify vt..调整,修改;修饰→modification n.32.profit n.& vt.利润,收益/获益;对...有用→profitable a. 有利可图的33.permission n.准许,许可,批准→permit vt..(permitted/permitting二、重点短语1.on( the) one hand, on the other hand 一方面,另一方面2. point out 指出3. on our way to producing a monster即将造出一个怪物on one’s/the way to doing 正在做某事的过程中4.at a much younger age than normal在比正常年龄小得多的年龄5. in general 一般来说,总体而言generally; generally speaking6. have/make a. scientific breakthrough 取得一个科学的突破7. the first mammal to be cloned successfully from an adult cell第一只被用成年动物细胞成功克隆的哺乳动物the first scientist to successfully clone the sheep第一位成功克隆出羊的科学家8. be praised for... 因-----而被表扬9. consider cloning human beings 思考克隆人类consider doing 考虑做某事10. concentrate on doing集中精力做某事focus one’s efforts on doing集中精力做某事try one’s best to do sth.11. with the intention of...以-----为目的或意图12. show no respect for human life不尊重人类生命13.toy with 戏弄14. push ahead with 义无反顾地进行,努力推行15. adopt someone else’s child领养别人的孩子16. totally transform my life彻底改变我的生活17. succeed in doing 成功做某事18. benefit mankind 造福人类benefit from the activities从这些活动中受益for one’s benefit= for the benefit of sb.为了某人的利益be of benefit to...= be beneficial to.. 对...有益19.deal with the consequences应付各种结果take/face the consequences of...承担...的后果as a /in consequence( of ...)结果/(因为...)20. for sale 供出售,待出售on sale 廉价出售,贱价抛售21. use up the Earth’s natural wealth耗尽地球的自然财富22. comment on ... = make comments on ...对....作出评价23. be in complete agreement with..... 完全同意....; 与...完全一致24. on a personal note 就个人而言in my opinion/viewas far as I am concernedfrom my point of viewfrom the view of my point25. die of heart failure/AIDS死于心脏病/艾滋病e across scientific terms遇到科学术语27. become a crop to be harvested成为待收割的庄稼28. as a whole 作为整体29. make sense to sb.讲得通,有道理make sense of sth.理解30. economic development 经济发展31. make it a crime to do human cloning 让克隆人成为一种犯罪32.put...in place把…放到合适的地方33.figure out想出,理解;计算出,34.in the field of science在科学领域35.the other day前几天,几天前,那天(用一般过去时)36.It’s (not) worth it.这事(不)值得。
矩阵逆学习资料woodbury公式关于矩阵逆的补充学习资料:Woodbury matrix identity本⽂来⾃维基百科。
the Woodbury matrix identity, named after Max A. Woodbury[1][2] says that the inverse of a rank-k correction of some matrix can be computed by doing a rank-k correction to the inverse of the original matrix. Alternative names for this formula are the matrix inversion lemma, Sherman–Morrison–Woodbury formula or just Woodbury formula. However, the identity appeared in several papers before the Woodbury report.[3]The Woodbury matrix identity is[4]where A, U, C and V all denote matrices of the correct size. Specifically, A is n-by-n, U is n-by-k, C is k-by-k and V is k-by-n. This can be derived using blockwise matrix inversion.In the special case where C is the 1-by-1 unit matrix, this identity reduces to the Sherman–Morrison formula. In the special case when C is the identity matrix I, the matrix is known innumerical linear algebra and numerical partial differential equations as the capacitance matrix.[3]Direct proofJust check that times the RHS of the Woodbury identity gives the identity matrix:Derivation via blockwise eliminationDeriving the Woodbury matrix identity is easily done by solving the following block matrix inversion problemExpanding, we can see that the above reduces to and, which is equivalent to .Eliminating the first equation, we find that , which can be substituted into the second to find. Expanding and rearranging, we have, or . Finally, we substitute into our , and we have. Thus,We have derived the Woodbury matrix identity.Derivation from LDU decompositionWe start by the matrixBy eliminating the entry under the A (given that A is invertible) we getLikewise, eliminating the entry above C givesNow combining the above two, we getMoving to the right side giveswhich is the LDU decomposition of the block matrix into an upper triangular, diagonal, and lower triangular matrices.Now inverting both sides givesWe could equally well have done it the other way (provided that C is invertible) i.e.Now again inverting both sides,Now comparing elements (1,1) of the RHS of (1) and (2) above gives the Woodbury formulaApplicationsThis identity is useful in certain numerical computations where A?1has already been computed and it is desired to compute (A+ UCV)?1. With the inverse of A available, it is only necessary tofind the inverse of C?1+ VA?1U in order to obtain the result using the right-hand side of the identity. If C has a much smaller dimension than A, this is more efficient than inverting A+ UCV directly. A common case is finding the inverse of a low-rank update A+ UCV of A (where U only has a few columns and V only a few rows), or finding an approximation of the inverse of the matrix A+ B where the matrix can be approximated by a low-rank matrix UCV, for example using the singular value decomposition.This is applied, e.g., in the Kalman filter and recursive least squares methods, to replace the parametric solution, requiring inversion of a state vector sized matrix, with a condition equations based solution. In case of the Kalman filter this matrix has the dimensions of the vector of observations, i.e., as small as 1 in case only one new observation is processed at a time. This significantly speeds up the often real time calculations of the filter.See also:Sherman–Morrison formulaInvertible matrixSchur complementMatrix determinant lemma, formula for a rank-k update to a determinantBinomial inverse theorem; slightly more general identity. Notes:1.Jump up ^ Max A. Woodbury, Inverting modified matrices, MemorandumRept. 42, Statistical Research Group, Princeton University,Princeton, NJ, 1950, 4pp MR381362.Jump up ^ Max A. Woodbury, The Stability of Out-Input Matrices.Chicago, Ill., 1949. 5 pp. MR325643.^ Jump up to: a b Hager, William W. (1989). "Updating the inverse of amatrix". SIAM Review31 (2): 221–239. doi:10.1137/1031049.JSTOR2030425. MR997457.4.Jump up ^Higham, Nicholas (2002). Accuracy and Stability ofNumerical Algorithms (2nd ed.). SIAM. p. 258. ISBN978-0-89871-521-7. MR1927606.Press, WH; Teukolsky, SA; Vetterling, WT; Flannery, BP (2007), "Section 2.7.3. Woodbury Formula", Numerical Recipes: The Artof Scientific Computing (3rd ed.), New York: CambridgeUniversity Press, ISBN978-0-521-88068-8External links:Some matrix identitiesWeisstein, Eric W., "Woodbury formula", MathWorld.src="///doc/2742834010661ed9ad51f3e6.html /wiki/Special:CentralAutoLogin/start?type=1x1" alt="" title="" width="1" height="1" style="border: none; position: absolute;" />Retrieved from"/doc/2742834010661ed9ad51f3e6.html /w/index.php?title=Woodbury_matrix_identity&oldid=627695139"Categories:Linear algebraLemmasSherman–Morrison formula(来⾃维基百科。
Unit 1 Learning for life时态用法分层练习一、单项选择1.There was an oil painting ________ in the corner. It ________ there for several days.A.laying; bad laid B.laid; had laidC.lying; had lain D.lying; had been lain【答案】C【详解】考查非谓语动词。
句意:角落里有一幅油画,它已经在那里好几天了。
第一个句子是there be句型,空格处需要非谓语动词,动词lie与an oil painting构成主动关系,故使用现在分词短语lying in the corner作后置定语修饰an oil painting,第二空根据句意和for several days可知,第二空动作先于was,使用过去完成时,lie (位于,处于)是一个不规则动词,过去式和过去分词为(lay, lain) ,故C正确。
2.I'm sure you will do better in the test because you___________ so hard this year.A.had been studyingB.have been studyingC.have studiedD.studied【答案】B【详解】考查动词的时态与语态。
句意:我相信你会在测试中做得更好,因为你今年一直很努力。
根据句子语境及this year,可知此处表达“作者一直学习很努力”,结合前面主句时态为一般现在时,可知此处用现在完成进行时。
选项B. have been studying符合题意,故选B。
3.The minister___________ a lecture on current affairs from 9 to 10 tomorrow morning.A.will have given B.has been given C.will give D.will be giving 【答案】D【详解】考查谓语动词。
Unit 6 Nurturing naturePeriod2Using language拓展练习原题版I.单元要点回扣练II.单句语法填空1. We believe the time and hard work_________(involve)in completing such an important project are worthwhile.2. Much of John Steinbeck's writing was concerned_________the land and the people of America.3. She_________(sleep)for 6 hours and still cannot wake up.4. In order to find the missing child, villagers_________(do)all they can over the past five hours.5. The boss_________(stay)in New York for four days last week. Now he is working in China.6. It is the third time that you_________(come)to our school.7. Henry feels rather tired because he_________(work)in the field for six hours.8. Up to now, the gifted child_________(win) three national prizes in music.9. I_________(look)for my lost book for three days, but I still haven't found it.10. The telephone_________(ring)for minutes, but no one_________(answer)it.III.阅读理解AWhen she first started learning about the climate change from one of her elders, Fawn Sharp was invited on a helicopter flight over the Olympic Mountains to survey the Mount Anderson glacier. But the glacier was gone, melted by the warming climate. Sharp had a deep sense of loss when she discovered the glacier wasn’t there any more.Loss is a growing issue for people working and living on the front lines of climate change. And that gave Jennifer Wren Atkinson, a fulltime lecturer at the University of Washington Bothell, US, an idea for a class.This term, she taught students on the Bothell campus about the emotional burdens of environmental study. She used the experiences of Native American tribes, scientists and activists, and asked her 24 students to face the reality that there is no easy fix—that “this is such an intractable problem that they’re going to be dealing with it for the rest of their lives.”Student Cody Dillon used to be a climate science skeptic(怀疑论者). Then he did his own reading and research, and changed his mind.Dillon wasn’t going into environmental work—he was a computerscience major. Yet, the potential for aworldwide environmental catastrophe seemed so real to him five years ago that he quit his job and became a fulltime volunteer for an environmental group that worked on restoration projects.Six months into the work, he decided that Atkinson’s class was just what he was looking for—a place where he could discuss his concerns about a changing climate.Atkinson said she hoped the class helped her students prepare themselves for the amount of environmental loss that will happen over their lifetimes.“We are already changing the planet—so many species are going to be lost, displaced or massively impacted,” she said. “The future isn’t going to be what they imagined.”1.Why did the author mention the case of Fawn Sharp?A.To lay a basis for Fawn Sharp’s further research.B.To prove Fawn Sharp’s work is similar to Atkinson’s.C.To lead into the issue of loss caused by climate change.D.To show scientists’ concern about the Mount Anderson glacier.2.What’s the main purpose of Atkinson’s class?A.To explore how different people deal with climate change.B.To get students more concerned about environmental issue.C.To find solutions to the Olympic Mountains environmental issue.D.To teach students how to conduct a research about environment.3.Which of the following best explains the underlined word “intractable” in paragraph 3?A.Simple.B.Difficult.C.Complicated. D.Interesting.4.How did Atkinson’s class influence Dillon?A.Dillon worked as a parttime volunteer for restoration projects.B.It made him realize a planetwide climate disaster would happen.C.It encouraged him to be more involved in environmental protection.D.It discouraged him to work on restoration projects for the environment.BScientists are preparing to launch the world’s first machine to clean up the planet’s largest mass of ocean plastic.The experts believe the machine should be able to collect half of the detritus in the patch—about 40,000 metric tons—within five years. In the past few weeks they have been busy welding together giant tubes that will sit on the surface of the sea and form the skeleton of the machine, creating the largest floating barrier ever made.The system, originally dreamt up by Mr. Slat, will be sh ipped out this summer to the Great Pacific Garbage Patch, between Hawaii and California, which contains estimated 1.8 trillion pieces of plastic. It will be the first ever attempt to tackle the patch since it was discovered in 1997.Mr. Slat was 16 and still at school when he was diving in Greece and first saw for himself the amount of plastic polluting the sea. “There were more bags than fish down there,” he recalls. Two years later he came up with a solution, quit university after six months and set up The Ocean Cleanup as a company. Mr. Slat says the first plastic to arrive on shore will be a major milestone. “We as humanity created this problem, so I think it’s also our responsibility to help solve it,” he says.The Great Pacific Garbage Patch(GPGP) covers an area of 1.6 million square kilometers and contains at least 79,000 tons of plastic, research found last month. Most of it is made up of “ghost gear”—parts of abandoned and lost fishing gear, such as nets and ropes—often from illegal fishing vessels.Ghost gear kills more than 100,000 whales, dolphins and seals each year, according to scientific surveys. Seabirds and other marine life are increasingly being found dead with stomachs full of small pieces of plastic. Creatures eat plastic discarded in the sea thinking it’s food but then starve to death because they are not feeding properly. Others are trapped and die of starvation or are strangled or suffocated by ghost gear.5.What does the underlined word “detritus” in the second paragraph probably mean?A.Waste. B.Ocean.C.System. D.Machine.6.Which one makes up most of the garbage in Pacific from the passage?A.Fishing vessels.B.Dolphins and seals.C.Giant tubes.D.Abandoned fishing gear.7.Why do some creatures in The Great Pacific Garbage Patch die of starvation?A.Because they are killed by ghost gear.B.Because they are suffocated by ghost gear.C.Because they don’t like eating plastic.D.Because they are not feeding properly.8.What is the main idea of the passage?A.A report about the death of marine life.B.News about the first machine to clean up ocean plastic.C.Information about ocean plastic.D.The reason for inventing a machine.IV.阅读七选五There are personal lifestyle changes that you can make that, in some combination, can help reduce your carbon impact. Not all are right for everybody. But applying just a few of them could make a difference.Move closer, to work.Transportation is one of the leading sources of greenhouse gas emissions (排放物). 1________ One way to dramatically cut transportation fuel needs is to move closer to work, use mass transportation, or switch to walking, cycling or some other modes of transport that does not require anything other than human energy.Consume less.2________ Whether by quitting an automobile or employing a reusable grocery sack, cutting back on consumption results in fewer fossil fuels being burned to extract, produce and ship products around the globe.3________A potentially simpler and even bigger effect can be made by doing more with less. Citizens of many developed countries are wasters of energy, whether by speeding in a gas-wasting vehicle or leaving the lights on when not in a room. Similarly, employing more efficient refrigerators, air conditioners and other appliances can cut electricity bills. 4 ________ You can turn the lights or your computers off when you leave the office.Stop cutting down trees.When purchasing wood products, such as furniture or flooring, buy used goods or, failing that, wood proved officially to have been sustainably (可持续地)harvested. The Amazon and other forests are more than the lungs of the earth, 5________A. Be energy efficient.B. Use few electrical appliances.C. But it doesn't have to be that way.D. Such efforts can also be usefully employed at work.E.They may also be humans' short-term hope for limiting climate change.F. The easiest way to cut back on greenhouse gas emissions is simply to buy less stuff.G. Citizens Spend more money on electricity to power devices when they're off than when they're onV.短文语法填空When we think about our daily habits and how they affect the environment, we focus 1__________ how much water and electricity we use, 2__________ if we choose a bike instead of a car when going outside. But even the 3__________(small) things can have a huge impact on our planet.Take plastic straws (吸管)for example. We often use them when 4__________(enjoy)a cold drink during our lunch or dinner, but Litterati, an app, shows that plastic straws are the sixth most common form of litter in the world. "Every day, Americans throw away 500 million plastic straws, 5__________are enough to circle the Earth twice, CNN reported. The plastic straws can't be recycled. And even worse, 6__________ takes up to 200 years for each one be broken down.To deal with the problem, a lawmaker in California, the US, 7__________(introduce)a bill late last month to reduce the use of plastic straws. Soon, 8__________ waiter in California who gives a customer a plastic straw without 9__________(request)will be breaking the law. The penalty (惩罚)will be up to six months in jail, a $1,000 fine or a combination of both, USA Today reported.“We need to raise 10__________(aware)of the issue of plastic straws and their effects on our waterways oceans," Ian Calderon, who introduced the bill, said in a statement.。
it 的用法(Ⅱ)语境自主领悟先观察原句后自主感悟1.There is no doubt that the earth is becoming warmer and that it is human activity that has caused this global warming rather than a random but natural phenomenon.2.It was a scientist called Charles Keeling who made accurate measurements of the amount of carbon dioxide in the atmosphere from 1957 to 1997.3.They also agree that it is the burning of more and more fossil fuels that has resulted in this increase in carbon dioxide.1.例1中的it is...that...为强调句型,在这个句型中,it没有意义,只是引出被强调的成分。
此处强调的是同位语从句的主语human activity。
2.例2中的it was...who...为强调句型,此处强调的是主句的主语a scientist。
被强调的成分是表示人的词,故也可用who。
3.例3中的it is...that...为强调句型,此处强调的是宾语从句的主语the burning of more and more fossil fuels。
一、强调句型的基本结构强调句型的基本结构为:it is/was+被强调部分+that/who+其他成分1.此结构中it 没有意义,只是引出被强调部分。
2.此强调句型只能强调主语、宾语、状语,不能强调谓语。
3.被强调的成分是表示人的词时用who/that,而被强调成分是其他时(事物、时间、地点等)只能用that。
选择性必修第三册Unit 6Nature in words考点1insist v. 坚称,坚决认为(教材P62)【拓展】【经典练】单句语法填空①(牛津高阶)I insist that you ________ (take) immediate action to put this right.②(剑桥高阶)Greg still insists (that) he ________ (do) nothing wrong.③(牛津高阶)She kept insisting ________ her innocence.单句表达④总之,只要你坚持这样做,你就会获得收获。
In conclusion, so long as ________________________,you will reap a harvest.考点2. bend v. 变弯曲(教材P63)【拓展】【经典练】写出withdraw在下列句中的词义①(剑桥高阶)I bent ________ and picked up the coins lying on the road.②(牛津高阶)He is bent on ________ (win) at all costs.③(牛津高阶)She managed to bend the mittee ________ her opinion.单句表达④(牛津高阶)他不能专心学习。
He couldn't ____________________ his studies.考点3.glare n. 刺眼的强光;怒视vi. 怒目而视;闪耀(教材P63) 【拓展】【经典练】选词填空(stare at/glare at/glance at)①(牛津高阶)I only had time to ____________ the newspapers.②(剑桥高阶)Don't ____________ people like that, it's rude.③(朗文当代)She ____________ him accusingly.单句表达④(牛津高阶)他没有喊叫,只是默默地怒视着我。
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONSGeneral Certificate of EducationAdvanced Subsidiary Level and Advanced LevelCHEMISTRYPaper 2 Structured Questions AS Core9701/02May/June 20061 hour 15 minutes Candidates answer on the Question Paper.Additional Materials: Data BookletREAD THESE INSTRUCTIONS FIRSTWrite your name, Centre number and candidate number on all the work you hand in.Write in dark blue or black pen in the spaces provided on the Question Paper.Y ou may use a pencil for any diagrams, graphs, or rough working.Do not use staples, paper clips, highlighters, glue or correction fluid.Answer all questions.Y ou may lose marks if you do not show your working or if you do not use appropriate units.A Data Booklet is provided.Y ou may use a calculator.The number of marks is given in brackets [ ] at the end of each question or part question.At the end of the examination, fasten all your work securely together.DO NOT WRITE IN THE BARCODE.DO NOT WRITE IN THE GREY AREAS BETWEEN THE PAGES.For Examiner’s Use12345Total9701/02/M/J/06© UCLES 2006For Examiner’s UseAnswer all the questions in the spaces provided.1 Mohr’s salt is a pale green crystalline solid which is soluble in water. Mohr’s salt is a ‘double salt’ which containstwo cations, one of which is Fe 2+,one anion which is SO 42–,and water of crystallisation.(a) The identity of the second cation was determined by the following test.Solid Mohr’s salt was heated with solid sodium hydroxide and a colourless gas wasevolved. The gas readily dissolved in water giving an alkaline solution.(i) What is the gas?..................................................................................................................................(ii) What is the formula of the second cation identified by this test?..................................................................................................................................(iii) In this test, a grey/green solid residue was also formed.Suggest a name or formula for this solid...................................................................................................................................[3] (b) The identity of the anion present in Mohr’s salt was confirmed by adding dilutehydrochloric acid followed by aqueous barium chloride to an aqueous solution of Mohr’s salt. A white precipitate was formed.Suggest the identity of the white precipitate.......................................................................................................................................[1] (c) When a double salt such as Mohr’s salt is made, the two individual salts are mixedtogether in a 1:1 molar ratio, dissolved in water and the solution crystallised.(i) Give the formula of each of the two salts that would be mixed to make the doublesalt, Mohr’s salt.salt 1 ...............................................salt 2 ...............................................9701/02/M/J/06© UCLES 2006ForExaminer’sUse 2 The unsaturated hydrocarbon ethyne (acetylene), C 2H 2, is widely used in ‘oxy-acetylenetorches’ for cutting and welding metals. In the torch, ethyne is burned in oxygen to produce a flame with a temperature of 3400 K.(a) Ethyne is a linear molecule with a triple bond, C ϵC, between the two carbon atoms. Draw a ‘dot-and-cross’ diagram of an ethyne molecule.[1] (b) When used for cutting or welding, ethyne is transported in cylinders which contain thegas under pressure. A typical cylinder has a volume of 76 dm 3 and contains ethyne gas at 1515 kPa pressure at a temperature of 25 °C.Use the general gas equation, pV = nRT , to calculate the amount, in moles, of ethyne inthis cylinder.[2] (c) In some countries, ethyne is manufactured from calcium carbide, CaC2, which isproduced by heating quicklime and coke together at 2300 K.CaO + 3C CaC 2 + COWhen water is added to the CaC2, calcium hydroxide, Ca(OH)2, and ethyne, C 2H 2, are produced. (i) Construct a balanced equation for the formation of ethyne from calcium carbide...................................................................................................................................(ii) Use this equation and your answer to part (b) to calculate the mass of CaC 2 whichwill react with an excess of water to produce enough ethyne to fill 100 cylinders ofthe gas.[3]Examiner’sUse© UCLES 20069701/02/M/J/069701/02/M/J/06© UCLES 2006For Examiner’s Use 4 Compounds containing the allyl group, CH 2=CHCH 2− , have pungent smells and are found in onions and garlic.Allyl alcohol, CH 2=CHCH 2OH, is a colourless liquid which is soluble in water.(a) Allyl alcohol behaves as an alkene and as a primary alcohol.Give the structural formula of the organic compound formed when allyl alcohol is (i) reacted with Br 2,(ii) heated under reflux with an acidified solution of Cr 2O 72– ions.[2] (b) When allyl alcohol is reacted with MnO 2 at room temperature, propenal, CH 2=CHCHOis formed.What type of reaction is this?......................................................................................................................................[1] (c) Allyl alcohol may be converted into propanal, CH 3CH 2CHO, by using a ruthenium(IV )catalyst in water.CH 2=CHCH 2OH ruthenium(IV ) catalyst CH 3CH 2CHOThe reactant and the product are isomers.What form of isomerism do they display? (1)9701/02/M/J/06© UCLES 2006For Examiner’s Use[Turn over (d) Allyl alcohol can be converted into propanal in two steps without the use of a ruthenium(IV ) catalyst.CH 2=CHCH 2OH step ICH3CH 2CH 2OH step II CH 3CH2CHOWhat reagents and conditions would be used for each step?step Ireagent(s) ........................................................................................................................condition(s) ...................................................................................................................... step IIreagent(s) ........................................................................................................................condition(s) ..................................................................................................................[4] (e) By considering your answers to (b) and (d), suggest what is unusual about the single-step reaction in (c).................................................................................................................................................................................................................................................................................[1] (f) Suggest the structural formula of the organic compound formed when allyl alcohol is (i) reacted with cold, dilute MnO 4– ions,(ii) heated under reflux with acidified MnO 4– ions.[3][Total: 12]9701/02/M/J/06© UCLES 2006ForExaminer’s Use5 Many organic reactions are substitution reactions in which the number of carbon atoms inthe organic compound is unchanged. (a) What is meant by the term substitution reaction ?................................................................................................................................................................................................................................................................................[1] (b) One example of a substitution reaction is the formation of an alcohol from ahalogenoalkane.(i) Write a balanced equation for the formation of ethanol from bromoethane...................................................................................................................................(ii) State the conditions for this reaction. (2)(c) In a few organic reactions, the product contains one more carbon atom than the startingmaterial.(i) Write the equation for a reaction in which the organic compound bromoethane,which contains two carbon atoms, is converted into an organic compound whichcontains three carbon atoms...................................................................................................................................(ii) State the conditions for this reaction. (2)(d)Ethanol may be converted into propanoic acid in a three-stage process which uses ethanol as the only organic compound.C 2H5OH step I K step II L step III C2H5CO2H(i) Give the structural formulae of the intermediate compounds K and L.K...............................................................................................................................L...............................................................................................................................(ii) State the reagent(s) used and give the essential condition(s) for step I and for step III.step Ireagent(s) .................................................................................................................condition(s) ...............................................................................................................step IIIreagent(s) .................................................................................................................condition(s) ................................................................................................................[6][Total: 11]BLANK PAGE。
高二英语上学期知识点复习【导语】由于高二开始努力,所以前面的知识肯定有一定的欠缺,这就要求自己要制定一定的计划,更要比别人付出更多的努力,相信付出的汗水不会白白流淌的,收获总是自己的。
作者高二频道为你整理了《高二英语上学期知识点复习》,助你金榜题名!1.高二英语上学期知识点复习paper复数:papers。
papers基本含义n.纸;纸张;报纸;文件;文献;v.贴壁纸;paper的第三人称单数和复数;I had papers relating to the children which my wife and I had to sign.我有一些关于孩子的文件需要我和妻子签字。
原型:paperpaper基本含义n.纸;纸张;报纸;文件;文献;v.贴壁纸;He wrote his name down on a piece of paper for me.他把他的名字写在一张纸上交给我。
第三人称单数:papers复数:papers现在分词:papering过去式:papered过去分词:papered2.高二英语上学期知识点复习1. Instead of spending your vacation on a bus, ... you may want to try hiking. Instead和instead 0f的用法2. Say "Hi" / "Hello" / "Thanks" to sb. (for me) 问候的句型3. Is anybody seeing you off? 进行时表将来4. She struggled and struggled, and could not get on her feet. (= keep struggling)5. You should not go rafting unless you know... unless引导条件状语从句,相当于if... not6. By staying at..., tourists can help the villagers make money so that they can take care of the fiver and the birds. 目的状语从句7. She was so surprised that she couldn't move. 结果状语从句8. Tree after tree went down, cut down by water. 过去分词作状语9. The next moment, the first wave swept her down, swallowing the garden. 现在分词作状语10. However, before she could think twice, the water was upon her. It didn't take long before the building was destroyed. before的用法3.高二英语上学期知识点复习【access】have access to有通道/有使用/有见到(某人/某物的机会或权益)【answer】answer to对……的回答【approach】approach to sth./ approach to doing sth.做某件事情的方法【attitude】attitude to sth.对待……的态度【contribution】make contributions to sth.对……做出奉献【damage】do damage to sth.对……造成破坏、破坏【devotion】devotion to sth.对……的奉献【entrance】entrance to某地方的一个入口【introduction】introduction to sth.对……的介绍【limit】the limit to sth.对……的一个限度/限制【objection】the objection to对……的反对【reaction】reaction to sth.对……东西的反应【response】response to sb./sth.对……人(或物)的回答/回复4.高二英语上学期知识点复习1. defend against保卫…以免受2.intruduce sb tosb 向某人介绍某人3.kiss sb on somepart亲吻某人的某个部位4.in defence 防备,保证5.together with 与某人一起6.be likely to 极可能…;有期望…7.reach one’s hand out to sth 把手伸出来取某物8.on the contrary 相反9.nod at sb 向某人点头10.greet sbwith/by 通过…向某人问候11.express one’s feelings表达某人的感情12. in general 总的来说;通常13.at a job fair 在求职会上14.be nervousabout 对…感到紧张15. at ease 舒服;快乐;自由悠闲16. lose face丢脸17.turn one’s back to 背对;背弃18.turn one’s head away 把头转过去19.be willing to 期望…. , 愿意….20. look upsetabout sth 对.. 感到沮丧5.高二英语上学期知识点复习1.Nobody knew that it was going to be different from other planets going to be different from other planets going round the sun.going round the sun 为现在分词短语定语,表示一样的动作。
用木头板凳和塑料板凳写作文Wood Bench vs. Plastic Bench.Which material is more durable?Wood is a natural material that is strong and durable. It is also resistant to rot and insects. However, wood can be damaged by water and fire.Plastic is a synthetic material that is also strong and durable. It is resistant to water and fire, but it can be damaged by sunlight.Which material is more comfortable?Wood is a warm and comfortable material to sit on. It is also naturally shock-absorbent, which makes it a good choice for seating in areas where people will be standing or sitting for long periods of time.Plastic is a cool and hard material to sit on. It is not as shock-absorbent as wood, so it can be uncomfortable to sit on for long periods of time.Which material is more affordable?Wood is a more expensive material than plastic. This is because wood is a natural resource that is in limited supply. Plastic is a synthetic material that can be produced in large quantities, which makes it more affordable.Which material is more sustainable?Wood is a sustainable material because it is a renewable resource. Trees can be replanted, which meansthat wood can be produced indefinitely.Plastic is not a sustainable material because it is made from fossil fuels, which are a non-renewable resource. Fossil fuels are also a major source of pollution.中文回答:木板凳和塑料板凳的耐用性对比。
我们该如何利用树木英语作文50字全文共10篇示例,供读者参考篇1Title: How can we make use of treesHello everyone! Today I want to talk about how we can use trees in our everyday lives. Trees are super important because they give us oxygen to breathe and they also provide a home for animals. So how can we make use of trees in our daily lives?First of all, we can use trees for shade. When it's hot outside, trees can give us a cool place to sit and relax. We can have a picnic under a tree or read a book in its shade. Trees also help to cool down our neighborhoods and reduce the need for air conditioning.Secondly, trees give us food. Have you ever eaten an apple from a tree? Or maybe you've had some maple syrup on your pancakes. These are all delicious things that come from trees. We can also use trees to make paper and wood for building things like houses and furniture.Trees are also important for our environment. They help to clean the air and absorb carbon dioxide. This helps to reduce global warming and make the air cleaner for us to breathe.So, let's all do our part to take care of trees and make use of them in our daily lives. We can plant trees in our community, recycle paper, and support companies that use sustainable wood products. Let's all work together to protect trees and the environment for future generations. Thank you for listening!篇2Title:Let's Make the World Greener TogetherHey everyone! Today I want to talk about how we can use trees to make our world a better place. Trees are so important for our planet. They give us oxygen to breathe and help keep the air clean. They also provide homes for animals and shade for us on hot days.One way we can use trees is by planting more of them. We can plant trees in our schoolyard, park, or even our own backyard. It's a fun and easy way to help the environment. We can also join tree planting events in our community to make a bigger impact.can water them regularly, remove any weeds around them, and protect them from pests. Trees need our help to stay healthy and strong.We can also use trees by learning more about them. We can read books or watch videos about different types of trees and their benefits. We can even go on a nature hike to see trees up close and learn how they grow.So, let's all work together to make the world greener by using trees in the best way possible. Remember, every tree makes a difference! Let's plant, protect, and learn about trees to make our planet a better place for all living things. Thank you for listening!篇3How to Use TreesHey guys! Today I want to talk about how we can use trees to make our world a better place. Trees are super important because they give us oxygen to breathe and they provide homes for animals. So, it's really important to take care of them and use them in the right ways.helps to clean the air and make our environment healthier. We can also use trees to make paper and wood for building things. But we need to be careful to not cut down too many trees because it can harm the environment.Another way we can use trees is by recycling paper. That means we can use paper over and over again instead of cutting down more trees. We can also use tree branches and leaves for composting, which helps to make soil healthier for growing plants.We can also use trees for fun activities like climbing or having a picnic under the shade of a tree. It's important to appreciate and respect trees because they do so much for us.In conclusion, trees are super important and we should all do our part to take care of them. Let's plant more trees, recycle paper, and enjoy the beauty of nature. By using trees in the right ways, we can help make our world a better place for everyone.篇4Title: Let's Make the Most of Trees!Hey friends! Do you know that trees are super cool? They give us oxygen to breathe, shade to play in, and fruits to eat. They are like the superheroes of nature! But do you know that we can do even more with trees?First of all, we can use trees to make paper. Paper is used for writing, drawing, and even packaging. By recycling paper, we can save more trees from being cut down. Isn't that amazing?Secondly, we can use trees to build houses and furniture. Wood from trees is strong and durable, making it perfect for construction. So next time you see a wooden house or a chair, remember that it came from a tree!Also, did you know that trees can help us save energy? By planting trees around our homes, we can lower the temperature and reduce the need for air conditioning. Trees are like natural air conditioners!Moreover, trees can provide homes for birds, squirrels, and other animals. By protecting trees, we are also protecting the habitats of these creatures. It's like creating a mini jungle in our own backyard!In conclusion, trees are not just plants standing in the ground. They are our friends and helpers. So let's make the mostof trees by using them wisely and taking care of them. Together, we can make the world a greener and healthier place for everyone!篇5Title: Let's Learn How to Use Trees Wisely!Hi everyone! Today, let's talk about how we can use trees in a smart way. Trees are super important because they give us oxygen, shade, and homes for animals. Here are some cool ways we can take care of trees and use them in a good way:1. Plant more trees: We can help the environment by planting more trees in our neighborhood. Trees help clean the air and make our community look beautiful.2. Don't waste paper: Paper is made from trees, so let's not waste it. We can use both sides of the paper when we draw or write, and recycle it when we're done.3. Enjoy nature: Trees are great for playing, climbing, and exploring. Let's enjoy being outside and spending time with nature. Remember to be gentle with trees and not hurt them.4. Make tree crafts: We can use fallen branches and leaves to make fun crafts like leaf rubbings, nature collages, or even bird feeders. Let's get creative and have fun with trees!5. Say no to cutting trees: Trees take a long time to grow, so let's not cut them down unless it's really necessary. We need to protect our forests and the homes of animals.Let's all be tree heroes and take care of our leafy friends. Trees are amazing, and they need our help to stay healthy. So let's make a plan to use trees in a smart way and protect our planet together! Let's go, tree team!篇6How to Use TreesHi everyone! Do you know how important trees are to us? Trees give us oxygen, provide us with shade, and even give us yummy fruits to eat! So, it's really important for us to take care of trees and make the most of them. Here are some fun ways we can use trees:1. Climbing treesWho doesn't love climbing trees? It's so much fun to climb up high and feel like you're the king or queen of the world! Butremember, always be safe when you're climbing trees. Make sure to have someone watching you and never climb too high.2. Building treehousesHave you ever imagined having your own secret hideout in a tree? By building a treehouse, you can have a cool place to hang out with your friends or just relax and read a book. Just make sure to ask for help from an adult when building it.3. Making art with leavesLeaves are not just for trees—they can also be used to create beautiful artwork! You can collect different leaves, press them, and use them to make leaf rubbings or even leaf animals. It's a fun way to be creative and appreciate nature.4. Planting treesOne of the best ways to use trees is by planting more of them! You can join tree-planting events in your community or even plant a tree in your backyard. It's a great way to give back to the environment and help make the world a better place.So, let's all do our part to take care of trees and make the most of them. They're our friends and we need them to stay happy and healthy. Let's give a big cheer for trees—hip, hip, hooray!篇7Title: How to Make the Most of TreesHey everyone! Do you know that trees are super important for our planet? They give us oxygen, provide homes for animals, and even give us yummy fruits to eat! So, let's talk about how we can make the most of trees and take care of them.First of all, we can plant more trees in our neighborhoods. Trees can help clean the air and make our environment more beautiful. We can plant a tree on special occasions, like Earth Day, Arbor Day, or even on our birthdays! It's a fun and meaningful way to give back to our planet.Secondly, we can use tree products wisely. We can recycle paper and cardboard so that we can save more trees from being cut down. We can also try to use less paper and use electronic devices more often. Remember, every sheet of paper comes from a tree, so let's try to use it wisely.Furthermore, we can learn more about different types of trees and their benefits. Some trees can give us medicine, some trees can provide shade, and some trees can even give us food. By understanding more about trees, we can appreciate them more and protect them better.Lastly, we can also take part in tree-planting activities or join environmental groups to help protect trees. We can organize tree-planting events with our friends and family or volunteer at local parks to take care of trees. Together, we can make a big difference!In conclusion, trees are amazing and we should do our best to take care of them. Let's plant more trees, use tree products wisely, learn about trees, and get involved in tree-planting activities. Let's show our love for trees and make our planet a greener and healthier place to live in. Thank you for listening!篇8Title: Let's Use Trees Wisely!Hey guys, do you know how awesome trees are? They give us oxygen, shade, and make our world look beautiful. But that's not all – we can also use trees in so many other cool ways. Let me tell you all about it!First of all, trees can give us yummy fruits. Who doesn't love apples, oranges, or bananas? Trees are the ones who make them for us. So, by planting more fruit trees, we can have anever-ending supply of delicious snacks!Next, trees can help us build stuff. Wood from trees is used to make our furniture, houses, and even paper. That's why we should always remember to recycle paper and not waste it. Trees work so hard to give us what we need, so we should do our part to take care of them too.Trees also provide homes for birds, insects, and other animals. By protecting trees and planting more of them, we can help save their habitats and make our environment a better place for everyone to live in.Lastly, trees can even help us clean the air and reduce pollution. They absorb harmful gases and release fresh oxygen into the atmosphere. So, the more trees we have, the cleaner our air will be.In conclusion, trees are super important and we should use them wisely. Let's plant more trees, recycle paper, and take care of our environment. Remember, when we take care of trees, they take care of us too!篇9Title: Let's Make the Most of Trees!Hey everyone! Today I want to talk about trees and how amazing they are. Trees are not just something we see outside, they are our friends! They give us so many things like fresh air, shade on hot days, and a home for birds and squirrels.But do you know that we can also learn English with trees? Yes, that's right! There are so many fun ways we can use trees to practice our English skills. Let me give you some ideas:1. Tree Identification: Go for a walk in the park or your neighborhood and try to identify different types of trees. Ask your parents or teachers to help you learn the names of the trees in English. You can even draw pictures of them and write their names in English.2. Tree Stories: Trees have been around for a long time and have seen so many things. Imagine what stories they could tell! Try writing a short story about a magic tree or a tree that can talk. This will help you practice your creative writing skills in English.3. Tree Vocabulary: Trees have lots of parts like leaves, branches, and roots. Learn the names of these parts in English and make flashcards to help you remember them. You can also practice spelling these words and use them in sentences.4. Tree Songs: Did you know there are songs about trees? Look up some tree-themed songs in English and sing along. This will not only improve your English pronunciation but also make learning more fun!So, let's all appreciate trees and use them to improve our English skills. Remember, trees are not just for climbing or picnicking under, they can also help us become better at English. Let's go out and explore the magical world of trees together!篇10How to Use TreesHey guys! Today, I want to talk to you about how we can use trees for lots of different things. Trees are super important for our planet and for us too, so it's really cool to learn about all the ways we can use them.One way we can use trees is for making paper. Trees are cut down and turned into paper that we use for writing, drawing, and making cool crafts. It's important to recycle paper too, so that we can save more trees from being cut down.Another way we can use trees is for building houses and furniture. Wood from trees is strong and durable, so it makesgreat material for building things. Just think about all the cool treehouses you can make!Trees also help us breathe by producing oxygen. They take in carbon dioxide and give us fresh air in return. So, it's important to plant more trees to keep our air clean and healthy.We can also use trees for food, like fruits and nuts. Apples, oranges, and almonds all come from trees. Yum!So, let's remember to appreciate and take care of trees because they are so amazing and give us so many great things. Let's plant more trees, recycle paper, and use wood responsibly. Trees rock!。
Unit 6 Nurturing natureUsing language一、单词拼写1.The c of oil in the world reaches 71 million barrels per day, which not only intensifies the energy crisis but worsens climate change as well.2.People were touched by the little girl’s keeping o regardless of difficulties in life. 3.He was always o (expecting good things to happen) about future, even when things were at their worst.4.His mother takes him to have art classes m .5.Millions and millions of acres have been transformed from forests into farmland because of the ever-growing c of food by an ever-growing population.6.Don’t be so pessimistic. You should be o about life.7.He was always o , even when things were at their worst.8.Light-hearted and o , she is the sort of woman to spread sunshine to people through her smile.9.How did they r when they heard the news?10.Explain what happened and how the person r__________ to the blame.11.The average of daily c of fruit and vegetables for a person is around 600 grams. 12.Global warming may be caused by burning fossil f , such as coal, oil, and natural gas. 13.He was always o about the future, even when things were at their worst.14.Many infectious diseases have been virtually e and hopefully Covid-19 will be got rid of in the future too.15.W the film star goes, there are always crazy fans waiting for her.16.Last but not least, why not keep a positive and o attitude at any time?17.We need to e (消除) bad habits and develop good ones. (根据中英文提示填空) 18.We can decrease our carbon foot print by cutting back on water c and not having our bedding and towels washed every day.19.Only an o person can face up to any barrier with a positive attitude and strong determination.20.Considering there are so many challenges to deal with, are you still o about the future of VR?21.Nuclear energy may overtake oil as the main f .22.Some interviewers would ask unexpected questions to see how the interviewee r to them.23.In spite of so many difficulties in his life, he remains o about his future. 24.Many people think that positive thinking is mostly about keeping one’s head in the sand and ignoring daily problems, trying to look o .25.The average daily c of fruit and vegetables is around 200grams.26.Money plays a c role in the administration and development of libraries.27.She was always o___________ even when things were at their worst.28.Even the future seems so gloomy, the young man holds a very o attitude: as long as he works hard, he will make a difference to the world.29.There is talk of raising the admission requirements to r the number of students on campus.30.The doctor advised him to reduce his alcohol c .31.In order to avoid the devastating effects of global warming, we should reduce the use of fossil f and develop clean energy technologies.32.I always tell my son, there are no great difficulties for a person who is brave, o , and willing to work hard!33.When at the hotel, we can reduce our impact by cutting back on water c and not having our bedding and towels washed every day.34.Turning off domestic appliances before going to sleep can reduce energy c . 35.According to a recent study, both the size and c habits of our eating companions can influence our food intake. (the act of using, eating, etc. something)36.One of the farmers had had a little 1 , a little pig and a colt. But all of them had been eaten by Nian.二、完成句子37.Practicing yoga is a good way for you (摆脱)your stress and worries, and find some inner peace.38.To freshen up the living room, we’ll (扔掉,处理掉) the old pillows and replace them with new ones.39.John wants to take up a job in another city, because the (月收入) in this city is not high.40.(无论这水看上去多么纯净),I do not want to drink it.41.Once you get addicted to drugs, you will have difficulty them. (摆脱,丢弃,扔掉)42.(不管你去到哪), the same things matter to everyone, family and friendship. 43.My mother paid (每月一次的拜访) to the poor family in the suburb.44.The smog in the air has colored the sky a smoky gray; it’s also given me a cough that I can’t (摆脱).45.(即使她是一个教授), she is not proud, and lives a simple and plain life. 46.Soldiers never gave in (不论敌人多么强大).47.—Do you think the instrument invented by the young man works well?—It is rather efficient (尽管很简易).48.(虽然我提出了一些很棒的主意), none of them were accepted. 49.(虽然我愿意帮忙), I don’t have much time.50.(无论发生什么事), we should believe that everything will turn out all right in the end.51.They won’t give up (即使) they should fail 10 times.52.What you need to do is (完全摆脱他们的控制).53.(无论我们的爱好是什么), the Internet can connect us with others who also enjoy doing them (即使) they live on the other side of the world.54.(无论我遇到什么困难), my friend will always stand by me like an angel. 55.(尽管很容易察觉) when students are interested, bored, or distracted, it is sometimes much harder to distinguish when students are troubled.56.As Aristotle said, no one would choose to live without friends, (即使) he had all other goods.三、阅读理解1A powerful earthquake hit Morocco on Friday night, killing over 2,500 people and causing huge damage over a large area. The quake was one of the most powerful ever recorded in Morocco. It’s also the country’s deadliest earthquake in over 60 years. So far, the earthquake is reported to have killed over 2,680 people. It has injured over 2,500 others. The earthquake was especially dangerous because it happened at night, when people were asleep in their homes.Marrakesh is a big city that’s popular with tourists. Many of its modern buildings seem to have survived the earthquake, but the old part of the city, Medina, was hit hard. It has buildings that are over 1,000 years old. Many of those buildings were demolished.Outside of Marrakesh, the earthquake caused even more damage. In the Atlas Mountains, the earthquake’s center, there are many small villages, some of which were nearly destroyed.Many of the people in the area live in simple houses made of mud bricks, which is a traditional way of building in Morocco. But it’s not strong enough to protect against earthquakes. Although the Moroccan government has laws that require buildings to be built more safely, these rules are often ignored.Rescue workers have been working hard to save those affected by the quake. In larger cities, rescue efforts seem to be going well. But it has taken a lot longer for help to reach remote areas in the mountains. Many of these villages are difficult to get to. The earthquake caused landslides, blocking roads, and making these places even more difficult to reach. In some areas, phone and electrical service were also knocked out, leaving these places completely cut off. That means that the local people in some remote areas have had to deal with the situation on their own. In some areas, people have been digging through the broken stones or bricks with their hands, trying to find survivors. Many people are sleeping outside, unsure if their houses are safe.Many outside countries have offered to help Morocco. Some countries have offered teams of experts; others have offered supplies.57.What do we know about the earthquake in Morocco?A.It killed 2,680 people.B.It occurred during the day.C.It was the deadliest in recent decades.D.It injured less than 2,500 people. 58.What does the underlined word “demolished” in paragraph 2 probably mean?A.destroyed B.decoratedC.protected D.constructed59.What is paragraph 4 mainly about?A.People living the quake-hit area are in urgent need of help from other countries.B.The current serious situation faced by people in disaster areas.C.Possible causes of the earthquake happening in Morocco.D.Reasons why the earthquake caused so much damage in Morocco.60.What is the text?A.A news report B.A short storyC.A research article D.A diary entry2It’s a good idea for families to talk about what they would do to escape a fire. You’ll want to talk about escape plans and escape routes, so let’s start here.An escape plan can help every member of a family get out of a burning house. The idea is to get outside quickly and safely. Smoke from a fire can make it hard to see where things are, so it’s important to learn and remember the different ways out of your home. If you live in an apartment building,you’ll want to know the best way to the stair or other emergency exits. If you’re in a room with the door closed when the fire breaks out, you need to take a few extra steps: Check to see if there’s heat or smoke coming in the cracks (裂缝) around the door.If you don’t see smoke — touch the door.If the door is hot or very warm — don’t open the door!If you don’t see smoke and the door is not hot — then use your fingers to lightly touch the doorknob (门把手). If the doorknob is hot or very warm — don’t open the door!If the doorknob feels cool, and you can’t see any smoke around the door, you can open the door very carefully and slowly. When you open the door, if you feel a burst of heat, or smoke pours into the room, quickly shut the door and make sure it is really closed. If there’s no smoke or heat when you open the door, go toward your escape route exit.61.Where does this passage probably come from?A.A safety guide book.B.A traffic guide book.C.A science fiction.D.A science report.62.The best title for the passage is .A.How to Deal with Smoke from a FireB.How to Make an Escape Plan and an Escape RouteC.The Best Way to Find the Stair or Other Emergency ExitsD.Steps on How to Escape a Fire in a Room with the Door Closed63.If you are in a room where there is a fire, the writer suggests that you should .A.get outside quickly and safelyB.stay in the room and wait for helpC.try to put out the fire by yourselfD.jump out of the room through windows64.What should you do if you find heavy smoke goes into the room?A.Find the nearest stair and run down.B.Close the door as quickly as possible.C.Open the door very carefully and slowly.D.Escape from your room as quickly as possible.四、语法填空1读下面短文,在空白处填入1个适当的单词或括号内单词的正确形式。
小学上册英语第1单元期末试卷英语试题一、综合题(本题有100小题,每小题1分,共100分.每小题不选、错误,均不给分)1.Igneous rocks are formed from the cooling of ______.2. Wall of China was built to protect against _____. The Grea3. A buffer solution helps maintain a constant ______.4.The Earth's atmosphere is essential for regulating temperature and protecting against ______.5.Understanding the role of plants in our environment is crucial for ______. (了解植物在环境中的作用对保护至关重要。
)6.What do you call the place where you go to borrow books?A. LibraryB. SchoolC. StoreD. ParkA7.Which instrument has keys and is played by pressing them?A. GuitarB. DrumsC. PianoD. FluteC8.What is the main character in a story called?A. ProtagonistB. AntagonistC. Supporting characterD. Narrator答案:A9.What shape has four equal sides?A. TriangleB. RectangleC. SquareD. Circle10. A baby cat is called a ______.11.My brother is a talented __________ (画家).12.I want to ___ (see/meet) my favorite singer.13.What do you call the process of changing from a caterpillar to a butterfly?A. TransformationB. MetamorphosisC. EvolutionD. Development14.If it rains, we will play __________ games inside. (室内的)15.Who is the main character in the story of "Peter Pan"?A. WendyB. TinkerbellC. Captain HookD. Peter Pan答案:D16.My cat enjoys sleeping in a sunny ______ (地方).17.____(Glaciers) can shape valleys over thousands of years.18.My sister has a ______ in her room.19. A ________ (植物) can be a beautiful decoration.20.The _______ (金鱼) swims in circles in its bowl.21. A garden can provide a habitat for various ______ and wildlife. (花园可以为各种动植物和野生动物提供栖息地。
【英语学习】第10周翻译练习之博物馆是否应当免费开放戊戌年六⽉廿⼆,浙江省博物馆Practice 371博物馆是否应当免费开放,这是当下热议的话题。
主流媒体和⾮营利机构的管理者也都在讨论这个话题。
有些⼈认为,博物馆不仅仅是娱乐休闲的地⽅,也是提供教育的地⽅,所以应该免费。
他们说他们理解博物馆取得藏品维护藏品要花很多钱,但⼀个对艺术感兴趣的⼈,不论⼤⼈、还是⼩孩,因为钱的原因⽽不能去观赏这些艺术品,这在道义上是不对的。
My:It's recently a controversial topic that the museums should either or not be open for free, which is talked about by both the main media and non-profit organizations. Some consider that they should be free for they are not only places for entertainment but also education. They say, although they understand the substantial cost of obtaining and preserving collections, it's immoral to make money the obstacle to appreciating those artworks of people interested in art ranging from children to adults.Teacher's:The debate over whether museums should be free is a big one right now. It's the source of a lot of discussion in the popular press and nonprofit boardrooms alike. Some people think that museums are not only there for enjoyment; they are education, and as such should be free. They say they appreciate the enormous costs involved in maintaining and obtaining collections, but the idea of a person or child interested in art not being able to view it because of cost is morally wrong.—-知识点—-1. A and B alike, A和B都…2. the debate over whether…is a big one right now, 在…上的讨论是当下热议的话题。
A Note on the Use of the Woodbury Formula To SolveCyclic Block Tri-Diagonal and Cyclic Block Penta-diagonalLinear Systems of EquationsMilan BatistaUniversity of Ljubljana, Faculty of Maritime Studies and TransportPot pomorščakov 4, 6320 Portorož, Slovenia, EUmilan.batista@Abdel Rahman A. Ibrahim KarawiaMathematics Department, Faculty of Science, Al-Qassim University,Buraidah 51452, Al-Qassim, KSA.abibka@.egAbstractThe article presents the theoretical background of the algorithms for solving cyclic block tridiagonal and cyclic block penta-diagonal systems of linear algebraic equations present in [1] and [2]. The theory is based on the Woodbury formula.Keywords: Linear algebraic systems; Block system; Cyclic systems; Periodic system; Tridiagonal systems; Penta-diagonal system; Woodbury formula1 IntroductionThe algorithms for solving the cyclic block tri-diagonal (CBTS) and cyclic block penta-diagonal systems (CBPS) of equations presented in ref [1], [2] are based on ad hoc introduction of the new unknown vector(s) which transform the original system into a non-cyclic system which can then be solved by standard methods. In this short paper the theoretical background of the algorithms based on the Woodbury formula ([3],[4]) will be given. Before proceeding it is perhaps necessary to emphasize that while the presenttreatment for solving CBTS differs only slightly from the method present in [5], the method for solving CBPS seems to be different from known methods.Now, the object of consideration is the cyclic block penta-diagonal system of linear algebraic equations Ax f = (1)where111112222233331111000n n n n nnnnn B C D E A A B C D E E A B C A D A B C C D E A B −−−−⎡⎤⎢⎥⎢⎥⎢⎥=⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦"""####%%%%#""""(2)is a cyclic block penta-diagonal system matrix, ()T12,,...,n x x x x = and()T12,,...,n f f f f = are unknown and known vectors (RHS vector), respectively, and4n ≥ is the number of equations. k A , k B , k C , k D and k E are matrices of size m m ×,and k f and k x are vectors of size m . In what follows, if not stated otherwise, all other matrices have size m m ×and all other vectors have size m . Also the vectors and matrices will be denoted by Roman lower-case and upper case letters, and scalars will be denoted by Greek lower-case letters. A unit matrix will be denoted as I and its dimension should be clear from the context; also from the context the meaning of the sign 0, which will be used for denoting scalar value or a null-matrix, should be clear.2 Cyclic block tri-diagonal systemWhen 0k k D E == the system (1) becomes a CBTS. To solve it the system matrix A is first de-composed into the form suggested by the Woodbury formulaT A AUV =+ (3)where is Ais an n n × block matrix, and U and V are 1n × block matrices. For systems under discussion a simple way to restore the off diagonal terms in (2) by (3) is determining that the product of the matrices U and T V in (3) is of the form[]11110000000000000000Tn n nn U X A UV V V U C X ⎡⎤⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥==⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦""#"##"##""(4)where matrices 1U , n U , 1V , n V , 1X , and n X should satisfy the following conditions 111111n n n n n n U V A U V C U V X U V X ==== (5)By introducing (4) into (3) one finds111222333111000000000000n n n nn n B X C AB C A B C AA B C A B X −−−−⎡⎤⎢⎥⎢⎥⎢⎥=⎢⎥⎢⎥⎢⎥⎢⎥−⎢⎥⎣⎦"""## ##%%%%#""""(6)The system (5) is four equations for six unknown matrices so its solution is not unique. A simple way to satisfy the first two of (5) is to choose 111n n n U I V A U I V C ααγ==== (7)where α and γ are non-zero scalars. Consequently,11n n X C X A γααγ==(8)Here the present derivation differs from that in [5] where the values 1αγ== are implicitly assumed. By (8) the matrix Atakes the same form as the matrix of the system (3) in ref [1]. By using (3) the system (1) becomes()TAUV x f +=Multiplying this with 1A − , where A is assumed to be non-singular, yields the system ()TI ZV x y += (9)where []1,...,Tn Z Z Z =, with matrices k Z and ()T12,,...,n y y y y =, with vectors k y , aregiven by 11Z A U y Af −−== (10)This is precisely the solution of the systems (6) and (7) used in ref [1]. From (9) the final solution of (1) is ()1T x I ZV y −=+ (11)where T I ZV + is assumed to be non-singular. With the Woodbury formula the inversion of this matrix is ()11T T I ZV I ZM V −−+=− (12)where T M I V Z =+ (13)is a matrix of order m m × which is assumed to be nonsingular. By (11) and (12) the solution x can be written in the form (eq 5 in [1]) x y Zu =− (14)where 1T u M V y −= is the vector. By using (7) one can easily find that 11n n M I C Z A Z γα=++ and 11T n n V y C y A y γα=+ so the vector u is computed by()()11111n n n n u I C Z A Z C y A y γαγα−=+++ (15)This is precisely the same vector as vector (15) in ref [1]. In this way the equivalence between the method used in [1] and when using the Woodbury formula is demonstrated.3 Cyclic block penta-diagonal systemWhen 121n n E E D D −=== the CBPS (1) can be solved by the same method as the CBTS. In general, however, to solve a CBPS the system matrix A may be de-composed into the following formT T A A UV PQ =++ (16)where Ais an n n × block matrix, and U , V , P and Q are 1n × block matrices. To restore the off diagonal terms in (2) the product of the matrices U and T V should be[]111111210000000000Tn n n nn nn U X Y E A UV V V V V U C D Y X −⎡⎤⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥==⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦""#"##"##"" (17)where matrices 1U , n U , 1V , 2V , 1n V −, n V , 1X , 1Y , n X , and n Y should satisfy the following conditions11111121111211n n n n n nn n nn n nU V A U V C U V E U V D U V X U V Y U V Y U V X −−======== (18)and the product of matrices P and T Q should yield[]22211110000000000000000Tn n n n P X E PQ Q Q P D X −−−⎡⎤⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥==⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦"""###"##"" (19)where matrices 2P , 1n P −, 1Q , n Q , 2X and 1n X − should satisfy the conditions 2211111211n n n n n n P Q E P Q D PQ X P Q X −−−−==== (20)By knowing U , V , P and Q, one, from (16), finds that T T A A UV PQ =−− or explicitly111112222233331111000000000n n n n nn nn n B X C Y D A XB C D E A B C AA B C X E A Y B X −−−−−−⎡⎤⎢⎥−⎢⎥⎢⎥=⎢⎥⎢⎥⎢⎥−⎢⎥−−⎢⎥⎣⎦"""####%%%%#""""(21)Both systems (18) and (20) are under-determinate. A simple way to satisfy the first two of (18) is to choose111n n n U I V A U I V C ααγ==== (22)where α and γ are a non-zero scalars. From the rest of (18) one obtains1121111n n n n n n V E V D X C Y D Y E X E αγγγααααγγ−======(23)Similarly, to satisfy first two of (20) one may set 22111n n n P I Q E P I Q D ββδδ−−==== (24)where β and δ are non-zero scalars, and, consequently,2112n n X D X E δββδ−−==(25)By (23) and (25) the matrix (21) has the form of matrix (5) in [2]. Now, by (16) the system (1) becomes()TT AUV PQ x f ++= (26)By multiplying this by 1A − , where A is assumed to be non-singular, one obtains the system ()TT I ZVWQ x y ++= (27)where []1,...,Tn Z Z Z =, with matrices k Z , []1,...,Tn W W W =, with matrices k W and()T12,,...,n y y y y =, with vectors k y , are given by111Z A U W A P y Af −−−=== (28)This is again precisely the solution of the systems (9) in ref [2]. From (27) the final solution of (1) is ()1T T x I ZV WQ y −=++ (29)whereT T I ZV WQ ++ is assumed to be non-singular. By nothing that[],,TT T T TZV WQ Z W V Q ⎡⎤+=⎣⎦the inversion of this matrix can be, by use of Woodburyformula, written as (this was corrected) ()[]11,,TT T T TI ZV WQ I Z W M V Q −−⎡⎤++=−⎣⎦ (30)where T T TTI V Z V W M Q ZI Q W ⎡⎤+=⎢⎥+⎣⎦(31)is a matrix of the order 22m m × which is assumed to be nonsingular. The solution x can therefore be written in the form (eq 8 in [2]) x y Zu Wv =−− (32)where 1T u M V y −= and 1T v M Q y −= are the vectors. By using (22) and (24) and (31) one can easily restore the system (17) in [2] for the determination of u and v . The equivalence between the method used in [2] and that using the generalized Woodbury formula is thus shown.4 ConclusionsIn the article the theoretical background of the method for solving cyclic block tri- and penta-diagonal linear systems present in ref [1] and [2] are given. In these references future details, implementation and numerical examples can be found. As is well known ([4],[5]) the attractiveness of the present method is that the cyclic block system (or any other system with the same off diagonal structure) can be solved through fewer operations than by using direct elimination or some direct sparse system algorithms (for example sparse 'skyline') if one poses an efficient way to solve the corresponding block diagonal system, for, besides solving this system, one must for CBTS additionally solve just the system of order m m× and in the case of CBPS just the system of order ×. Clearly, the present method works if the matrices A -- (12) and (31) -- and M 22m m--(13) and (31)--are non-singular. From the practical point of view non-singularity of matrices is tested by the program. Theoretical consideration is beyond the scope of the paper. The same is true also for the discussion of the optimal choice of parameters αβγ and δ, which remains an open question.,,References[1]Batista M. A Cyclic Block-Tridiagonal Solver, Advances in Engineering Software37, 2, (2006),: 69 - 74[2]Batista M. A Method for Solving Cyclic Block Penta-diagonal Systems of LinearEquations. arXiv:0803.0874v3 , 2008[3]Golub G.H., Van Loan C.H. Matrix Computations, Third Edition, Johns HopkinsUniversity Press, (1996)[4]Press W.H., Teukolsky S.A., Vetterling V.T., Flannery P.B. Numerical Recipes inC; The Art of Scientific Computing, Cambridge University Press, 1992[5]Yarrow M. Solving periodic block tridiagonal systems using the Sherman-Morrison-Woodbury formula. AIAA Computational Fluid Dynamics Conference, 9th, Buffalo, Technical Papers (A89-41776 18-02). Washington, DC, 1989, p. 188-196.。